Finite Group Databasebeta

← Group #13022252

Character table — Group #13022252

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444444444444444448888888888888888888888888888101010101010101010101010202020202020202020202020202020202020404040404040404040404040
order12222222222244444451010101010101010101010101010104444202020202020202020202020202020202020202020202020444444444444448888888888888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1−i−i−i−iiiii
χ51111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111−i−i−i−iiiii
χ81111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111iiii−i−i−i−i
χ9111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111
χ11111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i−i−iii
χ12111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iiiii−i−i
χ13111111111111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ14111111111111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ15111111111111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−i−i−i−iii
χ1711-1-1-111-111-1-1ii−i−ii−i1111111-1-1-1-1-1-11-1-11-1i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i11-1-1i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i
χ1811-1-1-111-111-1-1ii−i−ii−i1111111-1-1-1-1-1-11-1-11-1i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i11-1-1i−i-1-111−i−iii-1-111−i−iii1-1i−i-11−ii-11−ii
χ1911-1-1-111-111-1-1ii−i−ii−i1111111-1-1-1-1-1-11-1-11-1i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii-1-111−iiii−i−i-1-111−i−iii11-1-1-11−iii−i-11−ii1-1
χ2011-1-1-111-111-1-1ii−i−ii−i1111111-1-1-1-1-1-11-1-11-1i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii-1-111−ii−i−iii11-1-1ii−i−i-1-111-11−ii−ii1-1i−i-11
χ2111-1-1-111-111-1-1ii−i−ii−i1111111-1-1-1-1-1-11-1-1-11−iiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i11-1-1i−i11-1-1ii−i−i11-1-1ii−i−i-11−ii-11−ii-11−ii
χ2211-1-1-111-111-1-1ii−i−ii−i1111111-1-1-1-1-1-11-1-1-11−iiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i11-1-1i−i-1-111−i−iii-1-111−i−iii-11−ii1-1i−i1-1i−i
χ2311-1-1-111-111-1-1ii−i−ii−i1111111-1-1-1-1-1-11-1-1-11−iiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii-1-111−iiii−i−i-1-111−i−iii11-1-11-1i−i−ii1-1i−i-11
χ2411-1-1-111-111-1-1ii−i−ii−i1111111-1-1-1-1-1-11-1-1-11−iiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii-1-111−ii−i−iii11-1-1ii−i−i-1-1111-1i−ii−i-11−ii1-1
χ2511-1-1-111-111-1-1−i−iii−ii1111111-1-1-1-1-1-11-1-11-1−ii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii11-1-1−ii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii1-1−ii
χ2611-1-1-111-111-1-1−i−iii−ii1111111-1-1-1-1-1-11-1-11-1−ii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii11-1-1−ii-1-111ii−i−i-1-111ii−i−i1-1−ii-11i−i-11i−i
χ2711-1-1-111-111-1-1−i−iii−ii1111111-1-1-1-1-1-11-1-11-1−ii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i-1-111i−iii−i−i11-1-1−i−iii-1-111-11i−ii−i1-1−ii-11
χ2811-1-1-111-111-1-1−i−iii−ii1111111-1-1-1-1-1-11-1-11-1−ii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i-1-111i−i−i−iii-1-111ii−i−i11-1-1-11i−i−ii-11i−i1-1
χ2911-1-1-111-111-1-1−i−iii−ii1111111-1-1-1-1-1-11-1-1-11i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii11-1-1−ii11-1-1−i−iii11-1-1−i−iii-11i−i-11i−i-11i−i
χ3011-1-1-111-111-1-1−i−iii−ii1111111-1-1-1-1-1-11-1-1-11i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii11-1-1−ii-1-111ii−i−i-1-111ii−i−i-11i−i1-1−ii1-1−ii
χ3111-1-1-111-111-1-1−i−iii−ii1111111-1-1-1-1-1-11-1-1-11i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i-1-111i−iii−i−i11-1-1−i−iii-1-1111-1−ii−ii-11i−i1-1
χ3211-1-1-111-111-1-1−i−iii−ii1111111-1-1-1-1-1-11-1-1-11i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i-1-111i−i−i−iii-1-111ii−i−i11-1-11-1−iii−i1-1−ii-11
χ3322222222-2-2-2-22222-2-2222-2-2-2-222-2-2-2-2222000022-2-222-2-200000000000000002-22-222222-22-2-2-20000000000000000000000000000
χ3422222222-2-2-2-22222-2-2222-2-2-2-222-2-2-2-2222000022-2-222-2-20000000000000000-22-22-2-2-2-2-22-22220000000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-222222-2-2-2-222-2-2-2-22220000-2-222-2-22200000000000000002-22-2-2-2-2-22-22-2220000000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-222222-2-2-2-222-2-2-2-22220000-2-222-2-2220000000000000000-22-222222-22-22-2-20000000000000000000000000000
χ3722-2-2-222-2-2-2222i2i−2i−2i−2i2i222-2-2-2-2-2-222222-2-200002i2i−2i−2i−2i−2i2i2i00000000000000002-2-222i2i−2i−2i2-2-22−2i2i0000000000000000000000000000
χ3822-2-2-222-2-2-2222i2i−2i−2i−2i2i222-2-2-2-2-2-222222-2-200002i2i−2i−2i−2i−2i2i2i0000000000000000-222-2−2i−2i2i2i-222-22i−2i0000000000000000000000000000
χ3922-2-2-222-2-2-222−2i−2i2i2i2i−2i222-2-2-2-2-2-222222-2-20000−2i−2i2i2i2i2i−2i−2i00000000000000002-2-22−2i−2i2i2i2-2-222i−2i0000000000000000000000000000
χ4022-2-2-222-2-2-222−2i−2i2i2i2i−2i222-2-2-2-2-2-222222-2-20000−2i−2i2i2i2i2i−2i−2i0000000000000000-222-22i2i−2i−2i-222-2−2i2i0000000000000000000000000000
χ412-222-22-2-22-22-200000022-222-2-22222-2-2-2-2-2000000000000000000000000000022-220000-2-22-20000002-22-200002-22-2000000000000
χ422-222-22-2-22-22-200000022-222-2-22222-2-2-2-2-2000000000000000000000000000022-220000-2-22-2000000-22-220000-22-22000000000000
χ432-222-22-2-22-22-200000022-222-2-22222-2-2-2-2-20000000000000000000000000000-2-22-2000022-220000002i−2i2i−2i0000−2i2i−2i2i000000000000
χ442-222-22-2-22-22-200000022-222-2-22222-2-2-2-2-20000000000000000000000000000-2-22-2000022-22000000−2i2i−2i2i00002i−2i2i−2i000000000000
χ452-222-22-2-2-22-2200000022-2-2-22222-2-222-2-2-200000000000000000000000000002-2-2-20000-2222002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ462-222-22-2-2-22-2200000022-2-2-22222-2-222-2-2-200000000000000000000000000002-2-2-20000-222200−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ472-222-22-2-2-22-2200000022-2-2-22222-2-222-2-2-20000000000000000000000000000-222200002-2-2-2002-22-20000-22-220000000000000000
χ482-222-22-2-2-22-2200000022-2-2-22222-2-222-2-2-20000000000000000000000000000-222200002-2-2-200-22-2200002-22-20000000000000000
χ492-2-2-222-222-2-2200000022-222-2-2-2-2-2-222-2220000000000000000000000000000222-20000-2-2-220000002i−2i−2i2i00002i−2i−2i2i000000000000
χ502-2-2-222-222-2-2200000022-222-2-2-2-2-2-222-2220000000000000000000000000000222-20000-2-2-22000000−2i2i2i−2i0000−2i2i2i−2i000000000000
χ512-2-2-222-222-2-2200000022-222-2-2-2-2-2-222-2220000000000000000000000000000-2-2-220000222-20000002-2-220000-222-2000000000000
χ522-2-2-222-222-2-2200000022-222-2-2-2-2-2-222-2220000000000000000000000000000-2-2-220000222-2000000-222-200002-2-22000000000000
χ532-2-2-222-22-222-200000022-2-2-222-2-222-2-2-22200000000000000000000000000002-2220000-22-2-2002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ542-2-2-222-22-222-200000022-2-2-222-2-222-2-2-22200000000000000000000000000002-2220000-22-2-200−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ552-2-2-222-22-222-200000022-2-2-222-2-222-2-2-2220000000000000000000000000000-22-2-200002-222002-2-220000-222-20000000000000000
χ562-2-2-222-22-222-200000022-2-2-222-2-222-2-2-2220000000000000000000000000000-22-2-200002-22200-222-200002-2-220000000000000000
χ57444444444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ58444444444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-11111111111111111000000000000000000000000000000000000000000
χ59444444444444-4-4-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-144-4-411111111-1-1-1-1-1-1-1-111111111000000000000000000000000000000000000000000
χ60444444444444-4-4-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4441111111111111111-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ6144444444-4-4-4-44444-4-4-1-1-11111-1-11111-1-1-10000-1-111-1-11155−5−555−5−555−5−555−5−5000000000000000000000000000000000000000000
χ6244444444-4-4-4-44444-4-4-1-1-11111-1-11111-1-1-10000-1-111-1-111−5−555−5−555−5−555−5−555000000000000000000000000000000000000000000
χ6344444444-4-4-4-4-4-4-4-444-1-1-11111-1-11111-1-1-1000011-1-111-1-155−5−555−5−5−5−555−5−555000000000000000000000000000000000000000000
χ6444444444-4-4-4-4-4-4-4-444-1-1-11111-1-11111-1-1-1000011-1-111-1-1−5−555−5−55555−5−555−5−5000000000000000000000000000000000000000000
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χ67444-44-4-4-400004-44-400-11-15−55−5-115−55−51-110000-115−5-115−5ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19000000000000000000000000000000000000000000
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χ70444-44-4-4-40000-44-44004-4400004-40000-44-40000-4400-44000000000000000000000000000000000000000000000000000000000000
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χ72444-44-4-4-40000-44-4400-11-15−55−5-115−55−51-1100001-1−551-1−55ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19000000000000000000000000000000000000000000
χ73444-44-4-4-40000-44-4400-11-1−55−55-11−55−551-1100001-15−51-15−5ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.